Dynamic vertical interaction of a foundation–soil system generated by seismic waves

• The resonant phenomenon of the foundation is observed at certain excitation frequencies regardless of P waves or SV waves.
• Due to the pore water in soil medium, the vertical displacements of poroelastic model are smaller than those of elastic one.
• Comparing with a sealed boundary, an unsealed boundary of the poroelastic half-space contributes to a more significant vertical interaction.

Based on Biot's dynamic poroelastic theory, a foundation–soil interaction model is established to investigate the vertical vibrations of a rigid circular foundation on poroelastic soil excited by incident plane waves, including the fast P waves and SV waves. Scattering waves caused by the foundation and fluid–solid coupling due to the pore water in the soil are also considered in the model. The solution of the vertical vibrations of the foundation subjected to seismic waves are obtained by solving two sets of dual integral equations derived from the mixed boundary-value conditions. The different vertical vibrations of foundation rest on elastic and saturated half-space are compared. The influences of incident angle, permeability of soil and foundation mass on the vertical vibrations of the foundation are then discussed. The results show that resonant phenomenon of the foundation is observed at certain excitation frequencies; the effects of the pore water on the foundation vertical vibrations are significant. In addition, significant differences are found when the foundation is excited by P waves and SV waves, respectively.